Paper

The Cauchy problem for the Pavlov equation9

, and

Published 30 September 2015 • © 2015 IOP Publishing Ltd & London Mathematical Society
, , Citation P G Grinevich et al 2015 Nonlinearity 28 3709 DOI 10.1088/0951-7715/28/11/3709

Download Article PDF

Article metrics

161 Total downloads

Share this article

Author e-mails

pgg@landau.ac.ru

paolo.santini@roma1.infn.it

wudc@math.sinica.edu.tw

Author affiliations

1 L.D. Landau Institute for Theoretical Physics, pr. Akademika Semenova 1a, Chernogolovka 142432, Russia

2 Faculty of Mechanics and Mathematics, GSP-1, Lomonosov Moscow State University, 1 Leninskiye Gory, Main Building, 119991 Moscow, Russia

3 Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russia

4 Dipartimento di Fisica, Università di Roma 'La Sapienza', Piazz.le Aldo Moro 2, I-00185 Roma, Italy

5 Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Roma, Italy

6 Institute of Mathematics, Academia Sinica, 6F, Astronomy-Mathematics Building, No. 1, section 4, Roosevelt Road, Taipei 10617, Taiwan

Author notes

7 The author was partially supported by the Russian Foundation for Basic Research, grant 13-01-12469 ofi-m2, Russian Federation Government grant No 2010-220-01-077, by the program 'Leading scientific schools' (grant NSh-4833.2014.1), by the program 'Fundamental problems of nonlinear dynamics', Presidium of RAS, by the INFN sezione di Rome, and by the PRIN 2010/11 Prot. 2010JJ4KPA_004 of Roma 3.

8 The author was partially supported by NSC 101-2115-M-001-002.

Dates

  1. Received 26 January 2015
  2. Accepted 6 August 2015
  3. Published

Check for updates using Crossmark

Buy this article in print

Journal RSS
Sign up for new issue notifications
0951-7715/28/11/3709

Abstract

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data.

Export citation and abstract BibTeX RIS

Previous article in issue
Next article in issue

Recommended by Professor Alexander R Its

Footnotes

  • 9 

    An essential part of this work was made during the visit of the three authors to the Centro Internacional de Ciencias in Cuernavaca, Mexico in November–December 2012.

10.1088/0951-7715/28/11/3709